It sounds like you don't need a super powerful machine, and it also sounds like building your own doesn't seem to be something you want to do. Nor does it seem like you need a custom built machine as those are usually meant for those who know exactly what they want and want all the power they can get within their price range.
So, a prebuilt off the shelf computer is definitely the way you should go. Honestly I don't think anyone makes a bad desktop PC these days. You can always find horror stories if you look hard enough though.
So, for specifications you are going to want something with an Intel i3 or i5, or an AMD Ryzen 3 or Ryzen 5. Those are good midrange processors that will be in systems around your price range. For RAM you are probably going to only really need 4 GB, but 8 GB will make for a smoother experience and allow you to do more than one thing at a time. It won't be hard to find a system with 8 GB of memory in your budget. An SSD would be a great investment. As long as you are not storing a bunch of music, pictures, games, or movies something like a 256 GB SSD will be perfect for you. It will allow for quick boot times and a very quick and responsive machine. Larger drives are available and you might run into systems with smaller SSDs and standard hard drives for mass storage. Those are fine as well.
Unless you are thinking of traveling or that portability is something you want, a desktop will save you money and allow for more upgradability and less susceptibility to damage from dropping or spilling things. For desktops you have a few options though. You could go with an all-in-one which has the rest of the computer built into the back of the screen, the classic tower, or the small form factor computers that are like the size of a shoebox. Just remember that the smaller and more compact a computer is, usually the slower, less upgradable, and less easy to service computers are. As such I recommend a tower, but it is really up to you and what you want.
As for brands, pick something from someone reputable. Dell, HP, Acer, Asus, and Lenovo computers are good bets. They all have models with all of the above in your price range and are all very competitive with each other in terms of features and pricing.
Also, you didn't state that you were looking for a monitor at all, but that is another thing to consider. My advice is to go to a store where you can look at a few different models and pick one in your budget that you like best. You should consider a keyboard and mouse as well. Most computers are going to come with cheap ones that are okay-ish, but there are a lot better options that are going to be a lot more comfortable to type on for extended periods. Swing by the keyboard aisle and take a look at the options there if you feel so inclined.
So, I hope that helped explain a few things. Good luck picking out a good system. Feel free to come back with more questions if you have them.